It does matter, though, they have to be random primes and the resultant public key has to be unique. If the prime generation is predictable for a given piece of software, that is a huge weakness in it that is exploitable.

Again, you need to be careful tossing around words like “random” and “unique” in a mathematical discussion… Talking about two pairs being random doesn’t mean anything.

There are lots of ways to generate primes that are sufficiently unpredictable to be absolutely fine.

Thanks you - I’m heading for the beakthrough being a weakness (a predictability) in how the primes are calculated, rather than a breakthrough in factoring.

But you see, it doesn’t matter how the primes are calculated. As long as they are, in fact, prime, and are sufficiently large, you’re good to go. You could look them up in a book and that would be fine (obviously assuming you don’t re-use the same pair all the time). In practice it’s not that hard to find a couple of big primes computationally, as PS says.

Primes are one of the more magical elements of mathematics that are reasonably accessible without a whole lot of background, but the magic can be pretty counterintuitive. PS’s explanation is a good start.
It does matter, though, they have to be random primes and the resultant public key has to be unique. If the prime generation is predictable for a given piece of software, that is a huge weakness in it that is exploitable.

One thing I note is that the NSA don’t recommend RSA for US government communications… it rather suggests they think it insecure…

It does matter, though, they have to be random primes and the resultant public key has to be unique. If the prime generation is predictable for a given piece of software, that is a huge weakness in it that is exploitable.

Again, you need to be careful tossing around words like “random” and “unique” in a mathematical discussion… Talking about two pairs being random doesn’t mean anything.

There are lots of ways to generate primes that are sufficiently unpredictable to be absolutely fine.

Ah, but it is no longer a mathematical discussion, it is a software discussion. The generation of random numbers is a difficult business. If a particular piece of software or worse a random number generation function is compromised such that what it generates can be predicted, even within a range of possibilities, it fundamentally weakens the software.

I did kinda wonder if the breakthrough was to break an older form of encryption quickly so that they would be able to read oodles of stuff they had previously stored. Sure there’s time sensitive data, but a lot of it is not.

From the Snowden documents reveal that the NSA has hacked into the system for processing international transactions. EU lawmakers call now by the Commission, that the data exchange with the United States is placed on ice.
The press has reported that U.S. intelligence agencies have secretly tapped the Swift system, the system for international bank transfers. Now, a group of MEPs called for the immediate suspension of the joint EU-US program to track terrorist financing (TFTP).
“We can not continue with the loyal cooperation on data sharing with the U.S. authorities when NSA dark clouds hanging over our heads,” citing EUobserver the Belgian MEP Guy Verhofstadt.

Despite earlier US assurances that its Department of Defense does not “engage in economic espionage in any domain,” a new report suggests that the intelligence agency NSA spied on Brazilian state-run oil giant Petrobras.
Brazil’s biggest television network Globo TV reported that the information about the NSA spying on Petroleo Brasileiro SA came from Glenn Greenwald, the American journalist who first published secrets leaked by whistleblower Edward Snowden.
Globo TV aired slides from an NSA presentation from 2012 that revealed the agency’s ability to gain access to private networks of companies such as Petrobras and Google Inc.

A lavish Star Trek room he had built as part of his ‘Information Dominance Center’ is endlessly revealing

But a perhaps even more disturbing and revealing vignette into the spy chief’s mind comes from a new Foreign Policy article describing what the journal calls his “all-out, barely-legal drive to build the ultimate spy machine”. The article describes how even his NSA peers see him as a “cowboy” willing to play fast and loose with legal limits in order to construct a system of ubiquitous surveillance. But the personality driving all of this - not just Alexander’s but much of Washington’s - is perhaps best captured by this one passage, highlighted by PBS’ News Hour in a post entitled: “NSA director modeled war room after Star Trek’s Enterprise”. The room was christened as part of the “Information Dominance Center”:

RSA, the internet security firm, has warned customers not to use one of its own encryption algorithms after fears it can be unlocked by the US National Security Agency (NSA). In an advisory note to its developer customers, RSA said that a default algorithm in one of its toolkits could contain a “back door” that would allow the NSA to decrypt encrypted data. It “strongly recommends” switching to other random number generators. RSA is reviewing all its products.

The advice comes in the wake of New York Times allegations that the NSA may have intentionally introduced a flaw into the algorithm - known as Dual Elliptic Curve Deterministic Random Bit Generation - and then tried to get it adopted as a security standard by the US National Institute of Standards and Technology.

Green party politician Malte Spitz sued to have German telecoms giant Deutsche Telekom hand over six months of his phone data that he then made available to ZEIT ONLINE. We combined this geolocation data with information relating to his life as a politician, such as Twitter feeds, blog entries and websites, all of which is all freely available on the internet.

By pushing the play button, you will set off on a trip through Malte Spitz’s life. The speed controller allows you to adjust how fast you travel, the pause button will let you stop at interesting points. In addition, a calendar at the bottom shows when he was in a particular location and can be used to jump to a specific time period. Each column corresponds to one day.

The NSA facility, located 30 miles south of Salt Lake City in a town called Bluffdale, continuously uses 65 megawatts of electricity – enough to power a small city – at a cost of more than $1 million a month, the Journal reported.
The electrical problems, known as arc fault failures, create “fiery explosions, melt metal and cause circuits to fail,” one official told the newspaper.
“Documents and interviews paint a picture of a project that cut corners to speed building,” the Journal said. Backup generators have failed several times and the cooling system has yet to be tested, according to the newspaper.
An NSA spokeswoman told the Journal that “the failures that occurred during testing have been mitigated.” But the Journal said there is disagreement about the cause of the problems and whether proposed fixes will work.

MOSCOW (The Borowitz Report)—The N.S.A. leaker Edward Snowden today reached out to the United States government, offering to fix its troubled healthcare.gov Web site in exchange for immunity from prosecution.

Speaking from an undisclosed location in Russia, Mr. Snowden said he hacked the Web site over the weekend and thinks he is “pretty sure what the problem is.”

“Look, this thing was built terribly,” he said. “It’s a government Web site, O.K.?”

Mr. Snowden said that if an immunity deal can be worked out, “I can get to work on this thing right away—I don’t need a password.”

In addition to full immunity, Mr. Snowden said he is requesting that he be allowed to work from home.

At the White House, President Obama offered a muted response to Mr. Snowden’s proposal: “Edward Snowden is a traitor who has compromised our national security. Having said that, if he knows why we keep getting those error messages, that could be a conversation.”

Lawyers for a man described by the FBI as being the largest facilitator of child porn on the planet have mounted a fresh challenge to have him prosecuted in Ireland instead.

Eric Eoin Marques is wanted in the United States on four charges linked to website images described as being extremely violent, graphic and depicting the rape and torture of pre-pubescent children.

Defence barrister Remy Farrell told the High Court in Dublin he wished to make a submission to the Director of Public Prosecutions (DPP) on Section 15 of the Extradition Act, which relates to not extraditing a defendant when the alleged offence was committed in Ireland.

The DPP is considering a criminal file in the case.

Patrick McGrath, for the State, said he had no objection to the application.

Mr Justice John Edwards remanded Marques in custody for three weeks when the case will be mentioned again.